Related papers: Quantum Fields in Curved Spacetime: Non Global Hyp…
We study quantum and classical systems associated with the quantum corner symmetry group $\mathrm{QCS}=\widetilde{\mathrm{SL}}(2,\mathbb{R})\ltimes \mathrm{H}_3,$ which arises in the context of quantum gravity. We relate quantum observables…
Although there is general agreement that a removal of classical gravitational singularities is not only a crucial conceptual test of any approach to quantum gravity but also a prerequisite for any fundamental theory, the precise criteria…
We prove global hyperbolicity of spacetimes under generic regularity conditions on the metric. We then show that these spacetimes are timelike and null geodesically complete if the gradient of the lapse and the extrinsic curvature $K$ are…
Goal of this review is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, a…
This article presents an analysis of the extent to which local causal models or local realistic models of quantum theory (QT), including quantum field theory (QFT), are theoretically possible and practically feasible in light of the present…
We study quantum field theories which have quantum groups as global internal symmetries. We show that in such theories operators are generically non-local, and should be thought as living at the ends of topological lines. We describe the…
Free field theories on a four dimensional, globally hyperbolic spacetime, whose dynamics is ruled by a Green hyperbolic partial differential operator, can be quantized following the algebraic approach. It consists of a two-step procedure:…
We consider superfluidity and quantum vorticity in rotating spacetimes. The system is described by a complex scalar satisfying a nonlinear Klein-Gordon equation. Rotation terms are identified and found to lead to the transfer of angular…
Numerous approaches to a quantum theory of gravity posit fundamental ontologies that exclude spacetime, either partially or wholly. This situation raises deep questions about how such theories could relate to the empirical realm, since…
We argue that quantum gravity is nonlocal, first by recalling well-known arguments that support this idea and then by focusing on a point not usually emphasized: that making a conventional effective field theory (EFT) for quantum gravity is…
It has been discussed earlier that ( weak quasi-) quantum groups allow for conventional interpretation as internal symmetries in local quantum theory. From general arguments and explicit examples their consistency with (braid-) statistics…
We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…
The locality issue of quantum mechanics is a key issue to a proper understanding of quantum physics and beyond. What has been commonly emphasized as quantum nonlocality has received an inspiring examination through the notion of Heisenberg…
The formation of a naked singularity in a model of f(R) gravity having as source a linear electromagnetic field is considered in view of quantum mechanics. Quantum test fields obeying the Klein-Gordon, Dirac and Maxwell equations are used…
In this paper is considered a generalized quantization principle for the gravitational field in canonical quantum gravity, especially with respect to quantum geometrodynamics. This assumption can be interpreted as a transfer from the…
We propose a method to construct quantum theory of matter fields in a topology changing universe. Analytic continuation of the semiclassical gravity of a Lorentzian geometry leads to a non-unitary Schr\"{o}dinger equation in a Euclidean…
An ultralocal form of any classical field theory eliminates all spatial derivatives in its action functional, e.g., in its Hamiltonian functional density. It has been applied to covariant scalar field theories and even to Einstein's general…
In this work we establish a novel approach to the foundations of relativistic quantum theory, which is based on generalizing the quantum-mechanical Born rule for determining particle position probabilities to curved spacetime. A principal…
The framework of locally covariant quantum field theory is discussed, motivated in part using "ignorance principles". It is shown how theories can be represented by suitable functors, so that physical equivalence of theories may be…
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum…